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Nice try, what about this. 😂 The problem can easily be explained using Galileo's principle of inertia, Kepler's laws of planetary motion and Newton's universal law of gravitation. The accelerated motion of freefall was used to demonstrate why all objects fall in a vacuum at the same rate, regardless of there mass. The planets move with an orbital motion around a common centre of mass, called the barycentre. Galileo clearly showed that there was an attraction between objects of mass, by rolling objects down an inclined plane, and calculating the observed rate of acceleration in the 16th Century. The ocean tides are the result of the centrifugal effect of motion, whilst moving through a non-uniform gravitational field, that thankfully has an inverse square law geometry. It would be great to discuss this with you further, as you have an excellent approach to explaining physics simply and would be grateful for some positive support.
Further fact about Poincare's solution - he initially found a solution declaring that the 3 body problem was stable, applied for the prize, had his solution printed, but before it was distributed he found an error in his original solution and discovered that the 3 body problem was actually unstable. The original prints of the first incorrect solution were destroyed and no one knew that this had even happened until someone found a last surviving leaflet in the back of a cupboard. Even the best mathematicians in the world get things wrong sometimes.
It's understandable. Poincare was probably the last man to be considered a mathematician in all fields (mainly because there's WAY more fields now). Add that to the fact he genuinely could not draw and you can see why he made a mistake.
wrong--all the best mathematicians get things wrong , the best do not destroy their mistakes but sell them to a University for Historical purposes . Gauss was a bugger for erasing his traces also to make him look even smarter. Then, faced with his elegant polished equations , people could only wonder at how he had discovered them. Nasty piece of work that Gauss.
I love how succinct and powerful your statement that other sciences "felt like I was learning things. Whereas in physics, I was learning a totally new way of thinking." You're great at presenting these ways of thinking! :)
@@sterlingveilAgreed. Having studied biology I believe (molecular) biology does learn us about life interacting on different levels in which new sets of rules emerge, like natural selection and genetic drift. These transcendencies are fundamental to biology, but are particularly hard to understand as most people reason in a teleological way. In a way biology has thought us our world is not anthropocentric (men centered) and morality is an intrinsic quality of living beings. But I do not believe there superiority in either or any branch of science. Do what fascinates you!
I really like your style of science-communication. You don't oversimplify but manage to explain everything so well. Always fun watching your video's Jade!
@@upandatom Ma'am , If I place my hand flush against the wall and try to push the wall, does it mean I am applying force on the wall. Since FORCE = MASS X ACCELERATION ACCELERATION = VELOCITY / TIME VELOCITY = DISPLACEMENT / TIME Since there is no displacement between my hand and the wall therefore velocity becomes 0 and as a consequence Acceleration becomes 0 and hence Force becomes 0. So does that mean I am applying 0 force on the wall ? Am I right or wrong ma'am, please explain where I've gone wrong if I did. I searched a lot on the Internet and UA-cam but didn't find satisfactory answer for situation mentioned above
@@md.uzairahmed7774 im not that knowledgeable either but id say that depending on the wall and stuff there are a few factors, some of which are you pushing yourself away from the wall that push being (somewhat) absorbed by friction etc
Hailey's Comet is actually an interesting example to bring up, because it technically is part of an n-body problem. And yet, it behaves non-chaotically, as if the only two things that matter are the Sun and the Comet, allowing for the comment about a small error in estimating its position and momentum resulting in only a small error in predicting its return time, rather than it chaotically spinning off in some unpredicted direction due to that small error. So we must not only address the chaotic nature of the three body problem, but the way that this problem vanishes when one of the bodies is big enough. We calculate the moon's position by ignoring everything but the moon and the Earth, and we get pretty darn close, with small errors in the moon's estimated position and momentum leading only to small errors in estimating where it will be (relative to Earth) in the analytic 2-body equation. We do the same for the Earth and the Sun, and we then apply the Earth's estimated position plus the moon's relative estimated position to find the moon's position. It's a fairly simple system of equations that works because the Earth dominates the moon's orbital equation so much that the chaotic components vanish, and the Sun dominates the Earth's orbital equation so much that the chaotic components vanish.
Common factor is the Earth. There wouldn't be a problem if you calculated from the initial perspective of a different cosmology. Any one of the 30+ will do. Your contemporary cosmology creates problems that don't exist because false presumptions are the foundation of your equations. Try a different yet extremely simple, and once ubiquitous foundation, and it's an easy solve. Fits like a glove from every perspective. Answers every question like myriad puzzle pieces falling perfectly into place from the sky. Universal principles of physics are all you need. Don't break those laws for any reason, INCLUDING the "negative illusional perception of buoyancy" (gravity *cough*) and everything will make sense.
So far ...that's the nature of the problem, even seemingly stable systems can become chaotic over time. Our Earth, Moon Sun seems stable but many models predict the moon or earth being ejected at some point in the far future most likely caused by mercury causing havoc with one of the inner planets.
Excellent! In the early 1970s, I and my late friend, Dr. Walter J. Wild, who were physics majors at Illinois Institute of Technology, used IIT's Prime main-frame computer to do the 3-4-5 (initial right triangle) Three Body Problem. For the time, the solution--a crazy dance that ended with two bodies in orbit, and an expelled body that went off to infinity--that took an expensive number of minutes to complete, took an eternity compared to current super computers!
Beautiful closing remarks on how to think like a scientist. Today under massive pressures on grants, positions and so forth, scientists most often force themselves not to think as deeply as Poincare or other physicists at the time. I only wish we will continue to think like a scientist and you greatly help the next generation to do so. Great work! I hope you will cover Poircare's philosophy related to pragmatism sometime in the future.
I've been into pop-science for decades and been watching UA-cam physics channel videos for well over 10 years and this is the first time I've understood why the 3 body problem is so complicated. Your narration and animation of the saddle-points was extremely clear and made it very easy to understand. Thanks!
Her animations are fantastic. I'm not sure this was the intent here, but this video gave me an idea of what is meant when people say the universe is "shaped" like a saddle. It's not about what it looks like from 'outside' That's impossible as the universe is by definition everything, so there is no outside view. It's about how its forces contort its shape - i.e. the relationship between the objects of said universe.
@@AgentOccam To use the usual physical explanation for the curvature of the earth, instead of one, place two heavy objects on a stretched sheet, such that they are far enough away from each other that they do not roll together, but close enough so that there is a notable depression between them. There's a saddle point. You can even roll marbles around, and see how just slight variations on from where, or how fast, you roll them around, can cause them to wildly change their trajectory after hitting the saddle. And there you have the (that I've found) easiest, hands on, way to see the 3 body problem's... problem.
Random topic: the 2-3 problem. I'm a computer scientist, and over the years I've noticed a distinct pattern. LOTS of problems go from easy to hard when some parameter goes from 2 to 3 (eg 2SAT and 3SAT), just like this one. I wrote a small thing on these problems, and I wonder if there's already an answer for why this happens. Are you interested in taking a look?
The 2 -> 3 complication is not always the breaking point in other fields. Euler proved Fermat's last theorem for n= 3, and many others proved it for n= 4. The 3-body problem is not the only physics problem that can't be solved in closed form. The ballistics problem, i.e., trajectory of bullet, has no closed form solution in an atmosphere. (There are close approximations, by these have been yanked from Wikipedia).
@alohamark3025 absolutely! Lol I wasn't implying that 2 to 3 is the only breaking point, just that from a computation point of view, that seems to be a built in boundary for a lot of problems. I think it'd be really awesome to find more like it!
Looong time fan, and - wow - this was the best video on chaos theory - I always thought I understood it to a certain level, but I never put together the pieces of the saddle principle and Heisenberg. I always failed to appreciate the "how and why" of what makes things unpredictable and why more computational power isn't the answer. I'm sure your audience watches the same science communicator channels I do, and they're all great and enlightening, but your explanations just really make things fit and fill in the fogginess of some concepts. Thank you!
I like how this explains the history of the problem to give it some context. It starts with a simple premise and slowly builds on it to add complexity while keeping it approachable. I really like the visual style and animations of these videos. The presenting style has energy while also being calming and reassuring. Up and Atom has settled in to a friendly, professional look.
In this video you managed to talk about people whose names I'd heard before and teach me more about their accomplishments, clarified my understanding of a topic I often hear about but didn't understand the significance of, highlighted how solving the problem is not just a case of more&faster computers and told an entertaining story of how our understanding of the problem has evolved. You're a genius Jade, and this is yet another of your masterpieces!
Thank you so much for your videos! I am currently doing my PhD in Chemistry and I have the Feeling that most Chemist know too little about physics. And although the three body problem is a very important problem in quantum chemistry and we learn aboug it in class, I learned so much more about it from this video than from any textbook.
This takes me back to a very short period in the late 1980's, when I simultaneously discovered the Mandelbrot Set, Poincare's differential equation, Iterated function fractals, the Butterfly Effect, and all that amazing stuff that emerged when computers got smart and came into people's hands. Thanks for this, and you taught it so beautifully (in both senses).
For those of you who are curious, 2,500 Swedish krona (crowns) in 1889 is about US$78,500 on 2024-JUL-15. That's based on the fact that 2,500 krona could be exchanged for 35.5 ounces of gold in 1889, of which we have actual historical documentation. We use "troy ounces" today, so 35.5 becomes 32.27 troy ounces. Today's rate is $2,432.25 per troy ounce (equals 78,488.7075-ish).
I don't think that's the right way to calculate the current value. You calculated the value of the same gold amount, but the VALUE of the same thing (gold) can be different.
@@eddie1234544 An excellent point. Originally all money was attached to the gold standard. So prior to the 1930s, money was tied directly to gold whereas today we've tied money to all goods and services. To make a conversion from a 1880s currency to today, you need either "buying power" data or "gold equivalency" data. I only had the latter. By all means if anyone has a bill of lading showing the krona value of 10-20,000 carriages I'll gladly math us out a better estimate.
it's amazing that this video was suggested to me after watching a med school video on ECG heart waves, it made me look at heart dysrhythmias in a new light. also I loved that you mentioned that " it is still 100% deterministic but unpredictable", some channels omit such essential info leaving me confused at the end of the video. I also feel like I understand chaos theory better now. in conclusion, it's yet another beautiful video from Up and Atom
100% -- I honestly had assumed that all purely deterministic phenomena were ultimately predictable, assuming you had enough computation. This explanation helped me better understand what was going on.
When i think of chaos theory i think entropy. If i were to pour a pound of sand onto a highway that pound would disperse. There is no chance that the sand would somehow stay together. The wind, water, passing traffic and 1000 other factors would help disperse that sand everywhere. And i believe that even the 3 body problem needs to take entropy into account
That's one of the best explanatory vids I have seen in my life, and I really liked your uplifting and gentle way you presented everything....it made the whole experience both educational and fun... congrats and respect...!
This is the first video I see from your channel : thank you, really ! I'm no physician, but I love that "try to understand and predict and explain every bit of your world" part. I'm no absolute beginner (almost, though), so I love that you don't explain your subject as if I was 8 years old. You invite me to search and read more... I will
There are interesting talks and demonstrations using magnets with basins of attraction to draw maps of where the spots end up at a specific pole based on the position you release the magnet. There are highly chaotic areas versus some very stable areas with near-certain outcomes. Somewhat related, I think.
I love the idea of you catching your husband while he’s bench pressing to ask him how to pronounce someone’s name. We can almost hear him laugh warmly at the question. Clearly there is love for math and each other. ❤ And thank you for posting this on Nebula. 🎉
I teach a mathematical modeling class using computational calculus with MATLAB and cover some of this. Using a piece wise linear function in a for loop, you can set the interval to like .000001 seconds when modeling electric circuits, dynamics, falling objects. It is funny because some of the satellite orbit programs can take 15 minutes to run through to completion. Students have to set it to run and then go take a coffee break!
Excellent. I feel like I learned alot. Well paced, wonderfully narrated, and edited/curated. I definitely will be coming back, not only to further disect this video, but too see what else you have in store for me. Your means and technique for explanation, and presentation, are very nice. Easily approachable, learned and calculated. Deft and precise, thank you!
@@samo4003 well if i remember correctly, he is a computer scientist who discovered something about which jade once made a video... so his brains are atleast as good as hers
Watch her "The correct way to share a cake" video... her husband discovered the final algorithm she talks about (normally she puts a picture of the scientist, but since it was her guy here, she legit put their wedding photo lol 😂
I started my higher studying in biology as well than got into physics now I have master’s in pure mathematics, I guess that’s one example of unpredictability of nature of human judgment.
I read about the three body problem but couldn't quite understand it. This video really clarified what it is exactly. And, I was quite struck as to how it tied to Chaos theory.. Amazing explanation. Please keep up the excellent work!
Just discovered your channel, I love the way you explained the 3 body problem simply and concisely but still conveyed the problem thoroughly. And I admit I'm a sucker for an Aussie accent.. But besides that you just have a nice gentle voice. Have you ever considered teaching professionally? I imagine you'd be great. Anyways, I really enjoyed your video and am so glad I now understand the 3 body problem, even after I failed to grasp it from other youtubers' videos I've seen. Looking forward to learning more from your channel! Thank you! 😊
I also appreciate the clearly touted highlight, in lieu of your clear, concise, plus apt Coverage... whilst abiding a translation style that would truly allow for Mass Populace grasp along with the probable further interest... such as I personally believe, marks the very Key to our maximum advancement as a civilization, that henceforth, must achieve a reach through to the greater human population of our world. Altogether brilliant. Thanks
I also started as a biology major, but because interested in ecology and population modeling, which instantly put me into the realm of multi body problems. I devoted everything available at the time about these non linear equations This was just about the time the Lee and York paper introduced the term Chaos into mathematics. Exciting times, and I didn't even have to change my major in grad school.
Is this why in Quantum Physics, we start by considering events as random? It sounds like they are highly chaotic events, and our measurement intervals are quite large compared to particles movement speeds, so everytime we measure something, it's like we are past the point of diversion (besides that we affect the particles with every measurement).
Since we can't really verify it, there's no consensus on this. You could say the uncertainty comes from measurement, or it's just the nature of quantum particles. Either way, it's a limitation in how we understand the world. According to Poincare's theory, he said that our measurements can only get limited data, so the problem is unsolvable.
This is different. In Quantum mechanics there are random outcomes of simple measurements. The 3 body problem is deterministic, not random, and leads to unpredictability for long time periods or complex situations. It may be possible to construct a theory where the fundamental randomness of QM is not fundamental, but is produced by hidden chaos like the 3 body situation, but that is not the theory at the present time.
The three body problem of the Earth, Moon and Sun system, only remains relatively stable if you introduce the concept of a barycentre. I'm pretty sure it was Pierre Laplace that solved Newton's dilemma by suggesting the idea that the orbits would reset themselves after a certain number of cycles. Of course the planet Mercury doesn't conform to Newton's laws of gravitation, so we had to wait for Einstein to solve that dilemma. Thanks.
Absolutely delightful! Having majored in Astronomy, Physics, and Math 50+ years ago, the talk brought back pleasant memories of Dr. Williams' Intro to Celestial Mechanics. Thanks.
This is why I like Jade's approach of problem explanation. She makes the issue more structured and simplified. So, it seems that the map of gravitational effects was only in the (roughly) 2D plane of the solar system. Is there enough orbital variation out of the plane to account for unpredicted interactions between bodies?
Thank youuuu for your great work on this project 💕 it’s really nice to see you and your work in this space 💕 thank youuuu and I will definitely keep you updated on this journey ❤️ thank youuu and thank youuuu
What am amazing video & visuals!...I am now weighed down by the 'gravity' of the 3 body problem..;-) i am glad & thankful to you & youtube (for recommending ur channel to me)!
Forget about the gravity of the situation. The revolutionary idea behind the three body problem is our inertial concern. Why everything keeps moving in the first place and will continue to move forwards forever. Space tells matter how to move, and matter tells space how to curve. It all depends on whether we have enough time to make the calculations and complete our task. However, I don't have a french husband to help me pronounce the name, Pierre Laplace. 😂
I sometimes like to look at your videos for some ideas about how to describe a complicated technical thing I am working on. This video is a good example of a mix of interesting history, technically correct simplifications or simple cases for reasonable intuition, and - importantly - very reasonable and meaningful graphical representations of those intuitions. It’s often tiring to hear in your head the usual maxim to “shut up and calculate” and this gives me, at least, some permission to motivate things as one goes along and not be so demanding and sort of grouchy to the audience of the work. You really are very good at this. I would suggest, if I might, that spinning off from this video here and maybe a couple of old presentations about conservation of energy and stuff like that, to consider a presentation on Lagrange points for orbiting bodies. Various satellites used everyday by various common tools of modern life depend on this of course. Anyway, thanks for all the excellent videos over these years now.
classical physical equations and dynamics are still deterministic, but it doesn't mean that they are non-stochastic. stochasticity and determinism do not exclude each other. infinitesimal sensitivity to initial conditions means stochasticity and practical unpredictability, but the equations are still deterministic. but since the dynamics is extremely sensitive to the initial conditions AND the initial conditions cannot be know perfectly (even due to quantum mechanical reasons), this is really equivalent with indeterminism in practice. what really happens is that in classical mechanics in certain cases (e.g. a certain amount of degrees of freedom are needed) nonlinear equations emerge which can lead to the formerly mentioned infinitesimal sensitivity. it actually means some sort of remanifestation/reemergence (return) of stochasticity from the quantum realm. in quantum mechanics, stochasticity is inherent due to the (assumed) fundamental indeterminism. and interestingly, in both cases (quantum and classical) nonlinearty (i.e. self-referentiality) causes stochasticity, but meanwhile in classical mechanics it is contingent, in quantum mechanics it is inherent and thus necessary. this kind of remanifestation/reemergence from the quantum realm is not unique, since there is another example: wave nature. for bosons this is necessary (just think of Maxwell's equations where bunch of photons have the same wave nature as its constituting elements, i.e. photons), meanwhile for fermions this is contingent due to Pauli's exclusion principle (and when the wave nature remanifests/reemerges, it is already on the level of interactions). ps: it is interesting to realise that the core logic of postmodernism was already encoded in Newton's time in the form of this three body problem.
Post modernism as I see it is nihilism. That’s not Newtonian physics. So many people knowing that they can only know their part then conjecturing that there is no truth?!? Not only is the statement “there is no truth” self refuting given the starting conditions of logic, but the validity of “your truth” is in no way substantiated by ANY OF THIS. Post modernism and most of leftist ideology is hot garbage and a cancer on liberalism’s good name. Equity is not equality. Men are not women. The government is not your friend.
@@petevenuti7355 not in general. self-reference (self-referentiality) is a more general concept and category. nonlinearity is a special kind of self-referentiality. just like fractals are also examples for self-referentiality. probably this is why the phase space representations of nonlinear dynamical systems (i.e. attractors) can have fractal structure.
Amazing how simply turning the 2D line into the 3D Pringle instantaneously explained all my math-challenged mind will ever need to understand about the complexity of the problem. I don't have the math skills, but even I was able to see clearly where the problem explodes into near infinite possibilities...
What an excellent video explaining the problem. I've watched a number of videos surrounding it, but they often don't go into the uncertainty principle as to why we are unable to solve it..
If we ever have a robot teacher in every classroom, it needs to be modelled after Jade... I mean modelled with Jade's way of explaining things better than anyone else! 😅
The three-body problem is a classic example of a deterministic system that is incredibly complex to solve due to the sensitivity to initial conditions and the vast amount of information required. Determinism, in principle, implies that if we know the initial conditions of a system perfectly and have the exact laws governing it, we can predict its future states. However, in practice, especially with systems like the three-body problem, the sheer volume of data and the precision needed make such predictions impractically difficult. In the three-body problem, even the smallest uncertainties in initial conditions can lead to wildly different outcomes, a concept known as sensitivity to initial conditions or chaos. This makes long-term predictions extremely challenging, even though the system is theoretically deterministic. In essence, while determinism theoretically allows for the prediction of such systems, the practical limitations in measuring and computing the vast number of variables involved make it nearly impossible to achieve accurate long-term predictions.
You're getting better, Jade. You're on my favourite Aussi person list, along with; Margo Robbie, Daniel Riccardo, the Ozzie man, and Mick Dohan-among others. Keep the fun cartoons and humour up. (Next time don't use Poincare, use the Malcom character from Jurasic Park-his character was a chaos theory mathematician. -he's just more fun, and less work for your husband.) Cheers from the Pacific West Coast of Canada.
I can't emphasize enough how much I enjoy your videos. No one conveys enthusiasm for physics more charmingly than you and fills the short time with so much information.
THANK YOU for this video! I always wondered why we can't make predictions even if we had perfect measuring devices as it's still a deterministic system. You answered every one of my questions!
In highly complex systems, emergent behaviors can form. I would say the difference is if its a learning system, where with time there some sort of fitness function that guides how the entire system progresses in time, and if its not a learning system. I would say its like the Logic in Sudoku. If you have a square in sudoku that either a 1 or a 2 narrowed down, if you assume 1 and see what other squares must be, or if its a 2 and you see where other squares must be, where they intersect you can know what that square is without knowing what the original square value is. You can do this in games like minesweeper as well. So you can jump logical if A or B is true, and if A then C is true, and if B then C is true, then you can know C is true without knowing A or B truth value. Makes a powerful tool to break the hardest Sudokus when experimenting with the logic. Then came up handy on occasion in minesweeper. So that a 3 body is bound to following some equation maybe half true. Under conditions it could converge to an emergent behavior even though it seems wildly chaotic, the chaos itself will have emergent behaviors, like for example entropy. Things these equations may not have in them. And where fundamental theory of all learning systems maybe able to in time give them the tools to make their functions much more capable. Like a PDE can give a function and path, but in reality some kind of evolution of the system will occur and gravitate towards repeatable patterns. So something maybe chaotic, but if Saddle point if it goes on A side, or the B side, there maybe future states C that occur from both. So you can know the truth value of C without knowing if it went left or right on the saddle point. But this logic form is incredibly difficult to work with even in Sudoku to break the hardest puzzles.
Well, we have the 8+ Body problem. With orbits in the Sol system attaining resonance (google metronome resonance), it is only a matter of time till one of the Planets gets pulled out of orbit, the Professionals believe that planet will be Mercury.
There's some ideas thrown around that the Solar system has already ejected a planet in such a way. Evidence (with wrinkles, as always) is mounting that suggests that a large number of stellar systems like Sol's do so.
I actually got into this interesting mathematical discussion through synthesis, an instrument known as a chaos oscillator, based on the electronic circuit developed by Chuas. It’s a brilliant topic and I appreciate your ability to conceptualize ideas well beyond the orbit of my training and understanding. Thank you!
Excellent explanation. I don't think I've heard it explained so well. I have to admit the white dot shirt emblem had me a bit distracted. I was trying to figure out what that was!
Amazing video. I have seen some videos about the three body problem, but this is the first one which explained why such motion is fundamentaly unpredictible. Thanks!
I feel like the answer to this is a) consider a heirarchy of mass. The heaviest object is always the primary mass, and as you get lighter and lighter, each one is a servant to the heavier mass. b) This of this in terms of spacial distortions. Once you know what the basic path each body should normally follow, around the heaviest mass, then you can build a distortion map. You can then figure out what happens to the distortions each time distortions from one map intersects with distortions from the other map.
I have watched a great many videos taking about the Three Body Problem and its unsolvability, but I never felt like I truly understood why until now. Great video, thank you!
I believe that something else should be considered, synchronicity. There was an experiment conducted with boxes that have motors. Arms are attached to the motors. The arms are off center causing one end to swing out. Three such motors are placed so that the tips of the arms interfere with each other. The arms are random lengths and spin at random rates. When the tips happen to hit the motors reverse. After some time the three arms will find a way of bypassing each other regularly. This could explain how the Sun, Earth and Moon have solved the three body problem astro-mechanically.
Enjoyable learning, well presented and paced as always. Must say though I never such an upbeat attitude and bright eyed enthusiasm in my physics class. This is very different from another classic problem: You have 3 dead hitmen but only room in the trunk for two. What to do, what to do?
Super video. Having seen some of the drawings.. I suspect if Kandinsky and Miro had teamed up to draw in black and white, they might well have struggled to match Poincaré's level of abstraction.
I started in physics but switched to biology when my first modern physics class made me realize how dumb I actually am 😆. I still love physics but now I love it as a spectator now. You can't know how hard those problem sets are until you've actually worked on them, This channel is so great, thanks for making crazy hard stuff fun to learn about!
A really recommended beginners book to learn nonlinear dynamics and chaos from is Steven Strogatz’s “Nonlinear dynamics and chaos”. He also has a series of lectures on the topic here on UA-cam.
As someone who started out doing medicine, then switched to maths, and ultimately ended up doing mathematical epidemiology (which has a surprising amount in common with the topic you've been discussing here), I get how you felt about switching from biology to physics. Interestingly in my field a lot of people seem to have come from either maths or physics. Or veterinary science via statistics.
Great way to say "Henri Pointcarré" in French ! And you say it quite well! afterward). Great content. Thank you for sharing this video, as I hadn't historically connected Pointcarré's geometry to the 3 body problem.
We are living in amazing times We have digital tools that create visual images so clearly, that the equations can be seen as real images we can grasp in an instant.
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Excellently explained! Thank you!
Physical existence = structurally Dual Perspectives (plurality is within duality) = same differently!
Nice try, what about this. 😂
The problem can easily be explained using Galileo's principle of inertia, Kepler's laws of planetary motion and Newton's universal law of gravitation.
The accelerated motion of freefall was used to demonstrate why all objects fall in a vacuum at the same rate, regardless of there mass. The planets move with an orbital motion around a common centre of mass, called the barycentre.
Galileo clearly showed that there was an attraction between objects of mass, by rolling objects down an inclined plane, and calculating the observed rate of acceleration in the 16th Century.
The ocean tides are the result of the centrifugal effect of motion, whilst moving through a non-uniform gravitational field, that thankfully has an inverse square law geometry.
It would be great to discuss this with you further, as you have an excellent approach to explaining physics simply and would be grateful for some positive support.
😂 Yeah I can see that?
Great. That was fun. 😆
Its simple just add an updating variable each time they interact. The equation has to have a feedback loop.
Further fact about Poincare's solution - he initially found a solution declaring that the 3 body problem was stable, applied for the prize, had his solution printed, but before it was distributed he found an error in his original solution and discovered that the 3 body problem was actually unstable. The original prints of the first incorrect solution were destroyed and no one knew that this had even happened until someone found a last surviving leaflet in the back of a cupboard.
Even the best mathematicians in the world get things wrong sometimes.
"Sometimes" 😂
Tunnel vision is a real psychological problem that affects even the best of us
It's understandable. Poincare was probably the last man to be considered a mathematician in all fields (mainly because there's WAY more fields now).
Add that to the fact he genuinely could not draw and you can see why he made a mistake.
wrong--all the best mathematicians get things wrong , the best do not destroy their mistakes but sell them to a University for Historical purposes . Gauss was a bugger for erasing his traces also to make him look even smarter. Then, faced with his elegant polished equations , people could only wonder at how he had discovered them. Nasty piece of work that Gauss.
@@edwardmacnab354how he treated his sons
I love how succinct and powerful your statement that other sciences "felt like I was learning things. Whereas in physics, I was learning a totally new way of thinking." You're great at presenting these ways of thinking! :)
Oh, then you’ll love math! /gen
@@jessehammer123 If you think biology can't change the way you think, you should read some Dan Dennett!
@@sterlingveilare you talking about Daniel Dennett?
@@manahil558 Yep.
@@sterlingveilAgreed. Having studied biology I believe (molecular) biology does learn us about life interacting on different levels in which new sets of rules emerge, like natural selection and genetic drift. These transcendencies are fundamental to biology, but are particularly hard to understand as most people reason in a teleological way.
In a way biology has thought us our world is not anthropocentric (men centered) and morality is an intrinsic quality of living beings.
But I do not believe there superiority in either or any branch of science. Do what fascinates you!
I really like your style of science-communication. You don't oversimplify but manage to explain everything so well. Always fun watching your video's Jade!
Wow, thanks!
Came here to say the exact same thing!
@@upandatom
Ma'am ,
If I place my hand flush against the wall and try to push the wall, does it mean I am applying force on the wall.
Since FORCE = MASS X ACCELERATION
ACCELERATION = VELOCITY / TIME
VELOCITY = DISPLACEMENT / TIME
Since there is no displacement between my hand and the wall therefore velocity becomes 0 and as a consequence Acceleration becomes 0 and hence
Force becomes 0. So does that mean I am applying 0 force on the wall ?
Am I right or wrong ma'am, please explain where I've gone wrong if I did.
I searched a lot on the Internet and UA-cam but didn't find satisfactory answer for situation mentioned above
@@md.uzairahmed7774
im not that knowledgeable either but id say that depending on the wall and stuff there are a few factors, some of which are
you pushing yourself away from the wall
that push being (somewhat) absorbed by friction
etc
A very nice attempt Nouon, but I'm waiting for them to ask me the question. It's only polite to answer when someone asks you a question.
Hailey's Comet is actually an interesting example to bring up, because it technically is part of an n-body problem. And yet, it behaves non-chaotically, as if the only two things that matter are the Sun and the Comet, allowing for the comment about a small error in estimating its position and momentum resulting in only a small error in predicting its return time, rather than it chaotically spinning off in some unpredicted direction due to that small error.
So we must not only address the chaotic nature of the three body problem, but the way that this problem vanishes when one of the bodies is big enough.
We calculate the moon's position by ignoring everything but the moon and the Earth, and we get pretty darn close, with small errors in the moon's estimated position and momentum leading only to small errors in estimating where it will be (relative to Earth) in the analytic 2-body equation. We do the same for the Earth and the Sun, and we then apply the Earth's estimated position plus the moon's relative estimated position to find the moon's position. It's a fairly simple system of equations that works because the Earth dominates the moon's orbital equation so much that the chaotic components vanish, and the Sun dominates the Earth's orbital equation so much that the chaotic components vanish.
Terrific, detailed comment.
*Halley rhymes with “pal”, not “pail”
Common factor is the Earth. There wouldn't be a problem if you calculated from the initial perspective of a different cosmology. Any one of the 30+ will do. Your contemporary cosmology creates problems that don't exist because false presumptions are the foundation of your equations. Try a different yet extremely simple, and once ubiquitous foundation, and it's an easy solve. Fits like a glove from every perspective. Answers every question like myriad puzzle pieces falling perfectly into place from the sky. Universal principles of physics are all you need. Don't break those laws for any reason, INCLUDING the "negative illusional perception of buoyancy" (gravity *cough*) and everything will make sense.
@@aludred Perhaps you could demonstrate by example? I am not sure I follow what you're suggesting, here.
So far ...that's the nature of the problem, even seemingly stable systems can become chaotic over time. Our Earth, Moon Sun seems stable but many models predict the moon or earth being ejected at some point in the far future most likely caused by mercury causing havoc with one of the inner planets.
Excellent! In the early 1970s, I and my late friend, Dr. Walter J. Wild, who were physics majors at Illinois Institute of Technology, used IIT's Prime main-frame computer to do the 3-4-5 (initial right triangle) Three Body Problem. For the time, the solution--a crazy dance that ended with two bodies in orbit, and an expelled body that went off to infinity--that took an expensive number of minutes to complete, took an eternity compared to current super computers!
Beautiful closing remarks on how to think like a scientist.
Today under massive pressures on grants, positions and so forth, scientists most often force themselves not to think as deeply as Poincare or other physicists at the time. I only wish we will continue to think like a scientist and you greatly help the next generation to do so. Great work!
I hope you will cover Poircare's philosophy related to pragmatism sometime in the future.
I've been into pop-science for decades and been watching UA-cam physics channel videos for well over 10 years and this is the first time I've understood why the 3 body problem is so complicated. Your narration and animation of the saddle-points was extremely clear and made it very easy to understand. Thanks!
Her animations are fantastic. I'm not sure this was the intent here, but this video gave me an idea of what is meant when people say the universe is "shaped" like a saddle. It's not about what it looks like from 'outside' That's impossible as the universe is by definition everything, so there is no outside view. It's about how its forces contort its shape - i.e. the relationship between the objects of said universe.
@@AgentOccam To use the usual physical explanation for the curvature of the earth, instead of one, place two heavy objects on a stretched sheet, such that they are far enough away from each other that they do not roll together, but close enough so that there is a notable depression between them. There's a saddle point. You can even roll marbles around, and see how just slight variations on from where, or how fast, you roll them around, can cause them to wildly change their trajectory after hitting the saddle. And there you have the (that I've found) easiest, hands on, way to see the 3 body problem's... problem.
@@JesterMotley And even that is really only a 2D representation
Random topic: the 2-3 problem. I'm a computer scientist, and over the years I've noticed a distinct pattern. LOTS of problems go from easy to hard when some parameter goes from 2 to 3 (eg 2SAT and 3SAT), just like this one. I wrote a small thing on these problems, and I wonder if there's already an answer for why this happens. Are you interested in taking a look?
Some math explainers talk about this concept and proofs about the unsolvability of the 3 body problem.
@@erikb3799 do you have some specific videos to point to?
Yes, I'm interested
The 2 -> 3 complication is not always the breaking point in other fields. Euler proved Fermat's last theorem for n= 3, and many others proved it for n= 4. The 3-body problem is not the only physics problem that can't be solved in closed form. The ballistics problem, i.e., trajectory of bullet, has no closed form solution in an atmosphere. (There are close approximations, by these have been yanked from Wikipedia).
@alohamark3025 absolutely! Lol I wasn't implying that 2 to 3 is the only breaking point, just that from a computation point of view, that seems to be a built in boundary for a lot of problems. I think it'd be really awesome to find more like it!
Looong time fan, and - wow - this was the best video on chaos theory - I always thought I understood it to a certain level, but I never put together the pieces of the saddle principle and Heisenberg. I always failed to appreciate the "how and why" of what makes things unpredictable and why more computational power isn't the answer. I'm sure your audience watches the same science communicator channels I do, and they're all great and enlightening, but your explanations just really make things fit and fill in the fogginess of some concepts. Thank you!
I was offended by the pronunciation of Poincaré but was releaved to have a French man grunt it at me
LOL! Inasmuch as my pronunciation of anything or anyone French would offend, I was just pleased to know to whom she was referring.
I like how this explains the history of the problem to give it some context. It starts with a simple premise and slowly builds on it to add complexity while keeping it approachable.
I really like the visual style and animations of these videos. The presenting style has energy while also being calming and reassuring. Up and Atom has settled in to a friendly, professional look.
In this video you managed to talk about people whose names I'd heard before and teach me more about their accomplishments, clarified my understanding of a topic I often hear about but didn't understand the significance of, highlighted how solving the problem is not just a case of more&faster computers and told an entertaining story of how our understanding of the problem has evolved. You're a genius Jade, and this is yet another of your masterpieces!
Greatness is not just understanding a truth but figuring out how to better communicate it to all. Agree, Jade is a master communicator.
the gravity of the problem. very good Jade.
*Now I will get likes🤑🤑*
yeah, it was revolutionary too 😉
@@DwainDwight But all problems tend to have inertia, or more specifically a moment of inertia. 🤓
"it was when he added a third body that things took a turn"
Thank you so much for your videos! I am currently doing my PhD in Chemistry and I have the Feeling that most Chemist know too little about physics. And although the three body problem is a very important problem in quantum chemistry and we learn aboug it in class, I learned so much more about it from this video than from any textbook.
This takes me back to a very short period in the late 1980's, when I simultaneously discovered the Mandelbrot Set, Poincare's differential equation, Iterated function fractals, the Butterfly Effect, and all that amazing stuff that emerged when computers got smart and came into people's hands. Thanks for this, and you taught it so beautifully (in both senses).
For those of you who are curious, 2,500 Swedish krona (crowns) in 1889 is about US$78,500 on 2024-JUL-15. That's based on the fact that 2,500 krona could be exchanged for 35.5 ounces of gold in 1889, of which we have actual historical documentation. We use "troy ounces" today, so 35.5 becomes 32.27 troy ounces. Today's rate is $2,432.25 per troy ounce (equals 78,488.7075-ish).
But instead of gold, if you bought bitcoins for SEK 2500 back in 188 ... 🤔 oh.
@@dansihvonen8218 it didn't existed back then
@@onepointgameing2998 hence the cut off
I don't think that's the right way to calculate the current value. You calculated the value of the same gold amount, but the VALUE of the same thing (gold) can be different.
@@eddie1234544 An excellent point. Originally all money was attached to the gold standard. So prior to the 1930s, money was tied directly to gold whereas today we've tied money to all goods and services. To make a conversion from a 1880s currency to today, you need either "buying power" data or "gold equivalency" data. I only had the latter.
By all means if anyone has a bill of lading showing the krona value of 10-20,000 carriages I'll gladly math us out a better estimate.
it's amazing that this video was suggested to me after watching a med school video on ECG heart waves, it made me look at heart dysrhythmias in a new light.
also I loved that you mentioned that " it is still 100% deterministic but unpredictable", some channels omit such essential info leaving me confused at the end of the video.
I also feel like I understand chaos theory better now.
in conclusion, it's yet another beautiful video from Up and Atom
100% -- I honestly had assumed that all purely deterministic phenomena were ultimately predictable, assuming you had enough computation. This explanation helped me better understand what was going on.
When i think of chaos theory i think entropy.
If i were to pour a pound of sand onto a highway that pound would disperse. There is no chance that the sand would somehow stay together. The wind, water, passing traffic and 1000 other factors would help disperse that sand everywhere.
And i believe that even the 3 body problem needs to take entropy into account
7:57 Lagrange points!
Exactly 💯
*Yes bro I was just going to comment that*
If I remember correctly, it was Euler who found the first three, and Lagrance found L4 and L5 :)
@@MeesterG Exactly
6:04 Unstable fix point when the weight is highest. Great video!
That's one of the best explanatory vids I have seen in my life, and I really liked your uplifting and gentle way you presented everything....it made the whole experience both educational and fun... congrats and respect...!
Agreed!
This is the first video I see from your channel : thank you, really ! I'm no physician, but I love that "try to understand and predict and explain every bit of your world" part. I'm no absolute beginner (almost, though), so I love that you don't explain your subject as if I was 8 years old. You invite me to search and read more... I will
There are interesting talks and demonstrations using magnets with basins of attraction to draw maps of where the spots end up at a specific pole based on the position you release the magnet. There are highly chaotic areas versus some very stable areas with near-certain outcomes. Somewhat related, I think.
Doesn’t such a demonstration neglect other variables beyond magnetic attraction that influence where the magnets end up - such as friction?
Always love ur narration. Wonderful explanation ❤ so far thes best explanation on internet.
I love the idea of you catching your husband while he’s bench pressing to ask him how to pronounce someone’s name. We can almost hear him laugh warmly at the question. Clearly there is love for math and each other. ❤
And thank you for posting this on Nebula. 🎉
Pre-planned comic relief.
Is her husband single?
@@imarchello Did you "proof read" your comment?
I'm pretty sure it was a joke... Pretty sure
@@imarchello That's an entirely different 3-body problem right there.
I teach a mathematical modeling class using computational calculus with MATLAB and cover some of this. Using a piece wise linear function in a for loop, you can set the interval to like .000001 seconds when modeling electric circuits, dynamics, falling objects. It is funny because some of the satellite orbit programs can take 15 minutes to run through to completion. Students have to set it to run and then go take a coffee break!
15 minutes? When I did that stuff back in the 70's, it could take a day or more.
Excellent. I feel like I learned alot. Well paced, wonderfully narrated, and edited/curated. I definitely will be coming back, not only to further disect this video, but too see what else you have in store for me. Your means and technique for explanation, and presentation, are very nice. Easily approachable, learned and calculated. Deft and precise, thank you!
6:03 I love the implication that you just ambushed him while he was working out to ask him that lol
Solving the two birds with one stone equation, tell all the gentlemen suitors she's married, and show how strong he is in one go. 😋
6:04 What a chad, saying that name while lifting weights
... and also now, we know who is the brain of the family. 😅
@@samo4003 I didn't know brain and muscles were exclusive... 😅
@@igalbitan5096 maybe not mutually exclusive in the strictest sense, but inversely related in almost all cases.
@@samo4003 well if i remember correctly, he is a computer scientist who discovered something about which jade once made a video... so his brains are atleast as good as hers
Watch her "The correct way to share a cake" video... her husband discovered the final algorithm she talks about (normally she puts a picture of the scientist, but since it was her guy here, she legit put their wedding photo lol 😂
I started my higher studying in biology as well than got into physics now I have master’s in pure mathematics, I guess that’s one example of unpredictability of nature of human judgment.
😂
damn, you went all the way :)
And then you will become God?
@@trucid2 *what!?*
Social mobility in action ;)
I read about the three body problem but couldn't quite understand it. This video really clarified what it is exactly. And, I was quite struck as to how it tied to Chaos theory..
Amazing explanation. Please keep up the excellent work!
Just discovered your channel, I love the way you explained the 3 body problem simply and concisely but still conveyed the problem thoroughly. And I admit I'm a sucker for an Aussie accent.. But besides that you just have a nice gentle voice. Have you ever considered teaching professionally? I imagine you'd be great. Anyways, I really enjoyed your video and am so glad I now understand the 3 body problem, even after I failed to grasp it from other youtubers' videos I've seen. Looking forward to learning more from your channel! Thank you! 😊
Mathematicians solving the three body problem in particular configurations is like the famous mathematician joke "Assume a spherical cow in a vacuum".
Wonderful video! A nit pick 7:55 gives the impression that Poincare found the points discover by Euler and Lagrange.
I actually learned about LaGrange Points from a Superman comic when I was 12!
Thoughtful and simple explanation of a very difficult concept. Nicely done.
I also appreciate the clearly touted highlight, in lieu of your clear, concise, plus apt Coverage... whilst abiding a translation style that would truly allow for Mass Populace grasp along with the probable further interest... such as I personally believe, marks the very Key to our maximum advancement as a civilization, that henceforth, must achieve a reach through to the greater human population of our world. Altogether brilliant. Thanks
I also started as a biology major, but because interested in ecology and population modeling, which instantly put me into the realm of multi body problems. I devoted everything available at the time about these non linear equations This was just about the time the Lee and York paper introduced the term Chaos into mathematics. Exciting times, and I didn't even have to change my major in grad school.
Is this why in Quantum Physics, we start by considering events as random? It sounds like they are highly chaotic events, and our measurement intervals are quite large compared to particles movement speeds, so everytime we measure something, it's like we are past the point of diversion (besides that we affect the particles with every measurement).
Since we can't really verify it, there's no consensus on this.
You could say the uncertainty comes from measurement, or it's just the nature of quantum particles.
Either way, it's a limitation in how we understand the world.
According to Poincare's theory, he said that our measurements can only get limited data, so the problem is unsolvable.
You might as well make up random stuff yes, given this bumping particle phantasm has absolutely NO relation to reality.
This is different. In Quantum mechanics there are random outcomes of simple measurements. The 3 body problem is deterministic, not random, and leads to unpredictability for long time periods or complex situations.
It may be possible to construct a theory where the fundamental randomness of QM is not fundamental, but is produced by hidden chaos like the 3 body situation, but that is not the theory at the present time.
Thank you for the clear and simple explanation of the 3-body problem. It really helped me understand it.
The three body problem of the Earth, Moon and Sun system, only remains relatively stable if you introduce the concept of a barycentre.
I'm pretty sure it was Pierre Laplace that solved Newton's dilemma by suggesting the idea that the orbits would reset themselves after a certain number of cycles.
Of course the planet Mercury doesn't conform to Newton's laws of gravitation, so we had to wait for Einstein to solve that dilemma. Thanks.
Absolutely delightful! Having majored in Astronomy, Physics, and Math 50+ years ago, the talk brought back pleasant memories of Dr. Williams' Intro to Celestial Mechanics. Thanks.
This is why I like Jade's approach of problem explanation. She makes the issue more structured and simplified. So, it seems that the map of gravitational effects was only in the (roughly) 2D plane of the solar system. Is there enough orbital variation out of the plane to account for unpredicted interactions between bodies?
We wait 4 months for a masterpiece😢😢
Worth it.
A masterpiece worth waiting for
agreed
She is
Thanks Jade for so you're excellent content.
@10:25 I wanted to cry for no apparent reason... physics is beautiful
Kudos to the animator!
Best description of a complex system, without (I think) telling people it is a a complex system. Either way just a beautiful explanation
Thank youuuu for your great work on this project 💕 it’s really nice to see you and your work in this space 💕 thank youuuu and I will definitely keep you updated on this journey ❤️ thank youuu and thank youuuu
What am amazing video & visuals!...I am now weighed down by the 'gravity' of the 3 body problem..;-) i am glad & thankful to you & youtube (for recommending ur channel to me)!
9:10 chaos will later lead to ... Fractals.
Indeed, the solution to many nonlinear systems of equations lie on an invariant set, aka strange attractor, which has a fractal dimension. 🙂
Actually the field of solutions of 3 body problem is a fractal =_=
@@Rin8Kin further more surprised she did not mention it at all ...
And pseudo random number generators.
Only through Planck-phire and golden ratio do we each save our soul.
Forget about the gravity of the situation.
The revolutionary idea behind the three body problem is our inertial concern.
Why everything keeps moving in the first place and will continue to move forwards forever.
Space tells matter how to move, and matter tells space how to curve.
It all depends on whether we have enough time to make the calculations and complete our task. However, I don't have a french husband to help me pronounce the name, Pierre Laplace. 😂
You just answer a question I search only hours a go😂
I sometimes like to look at your videos for some ideas about how to describe a complicated technical thing I am working on. This video is a good example of a mix of interesting history, technically correct simplifications or simple cases for reasonable intuition, and - importantly - very reasonable and meaningful graphical representations of those intuitions. It’s often tiring to hear in your head the usual maxim to “shut up and calculate” and this gives me, at least, some permission to motivate things as one goes along and not be so demanding and sort of grouchy to the audience of the work. You really are very good at this. I would suggest, if I might, that spinning off from this video here and maybe a couple of old presentations about conservation of energy and stuff like that, to consider a presentation on Lagrange points for orbiting bodies. Various satellites used everyday by various common tools of modern life depend on this of course. Anyway, thanks for all the excellent videos over these years now.
Thanks!
classical physical equations and dynamics are still deterministic, but it doesn't mean that they are non-stochastic. stochasticity and determinism do not exclude each other. infinitesimal sensitivity to initial conditions means stochasticity and practical unpredictability, but the equations are still deterministic. but since the dynamics is extremely sensitive to the initial conditions AND the initial conditions cannot be know perfectly (even due to quantum mechanical reasons), this is really equivalent with indeterminism in practice.
what really happens is that in classical mechanics in certain cases (e.g. a certain amount of degrees of freedom are needed) nonlinear equations emerge which can lead to the formerly mentioned infinitesimal sensitivity. it actually means some sort of remanifestation/reemergence (return) of stochasticity from the quantum realm. in quantum mechanics, stochasticity is inherent due to the (assumed) fundamental indeterminism. and interestingly, in both cases (quantum and classical) nonlinearty (i.e. self-referentiality) causes stochasticity, but meanwhile in classical mechanics it is contingent, in quantum mechanics it is inherent and thus necessary.
this kind of remanifestation/reemergence from the quantum realm is not unique, since there is another example: wave nature. for bosons this is necessary (just think of Maxwell's equations where bunch of photons have the same wave nature as its constituting elements, i.e. photons), meanwhile for fermions this is contingent due to Pauli's exclusion principle (and when the wave nature remanifests/reemerges, it is already on the level of interactions).
ps: it is interesting to realise that the core logic of postmodernism was already encoded in Newton's time in the form of this three body problem.
Self-referential equals non-linearity please explain?
Post modernism as I see it is nihilism. That’s not Newtonian physics.
So many people knowing that they can only know their part then conjecturing that there is no truth?!? Not only is the statement “there is no truth” self refuting given the starting conditions of logic, but the validity of “your truth” is in no way substantiated by ANY OF THIS.
Post modernism and most of leftist ideology is hot garbage and a cancer on liberalism’s good name. Equity is not equality. Men are not women. The government is not your friend.
@@petevenuti7355 not in general. self-reference (self-referentiality) is a more general concept and category. nonlinearity is a special kind of self-referentiality. just like fractals are also examples for self-referentiality. probably this is why the phase space representations of nonlinear dynamical systems (i.e. attractors) can have fractal structure.
Yay you posted again I've been waiting ages 😁
Wait till they find out about the forth body in my basement.... wait what? Who said that?
Did the FBI visit you already
@@benyomovod6904If it's still moving the FBI won't help
I lolled about this
That's a third AND fourth body problem.
😂
Amazing how simply turning the 2D line into the 3D Pringle instantaneously explained all my math-challenged mind will ever need to understand about the complexity of the problem. I don't have the math skills, but even I was able to see clearly where the problem explodes into near infinite possibilities...
What an excellent video explaining the problem. I've watched a number of videos surrounding it, but they often don't go into the uncertainty principle as to why we are unable to solve it..
If we ever have a robot teacher in every classroom, it needs to be modelled after Jade...
I mean modelled with Jade's way of explaining things better than anyone else! 😅
Jade's ability to communicate is extremely high, and I agree, should be the initial standard model.
The three-body problem is a classic example of a deterministic system that is incredibly complex to solve due to the sensitivity to initial conditions and the vast amount of information required. Determinism, in principle, implies that if we know the initial conditions of a system perfectly and have the exact laws governing it, we can predict its future states. However, in practice, especially with systems like the three-body problem, the sheer volume of data and the precision needed make such predictions impractically difficult.
In the three-body problem, even the smallest uncertainties in initial conditions can lead to wildly different outcomes, a concept known as sensitivity to initial conditions or chaos. This makes long-term predictions extremely challenging, even though the system is theoretically deterministic. In essence, while determinism theoretically allows for the prediction of such systems, the practical limitations in measuring and computing the vast number of variables involved make it nearly impossible to achieve accurate long-term predictions.
The "gravity" of the 3 body problem
You're getting better, Jade. You're on my favourite Aussi person list, along with; Margo Robbie, Daniel Riccardo, the Ozzie man, and Mick Dohan-among others. Keep the fun cartoons and humour up. (Next time don't use Poincare, use the Malcom character from Jurasic Park-his character was a chaos theory mathematician. -he's just more fun, and less work for your husband.)
Cheers from the Pacific West Coast of Canada.
I can't emphasize enough how much I enjoy your videos. No one conveys enthusiasm for physics more charmingly than you and fills the short time with so much information.
When you rolled out your French husband, I naturally began to wonder if you would be rolling out other husbands for more accurate pronunciation.
Dude WHAT
Ha ha 😂
I have tried to pronouce Henri Poincaré the exact same way your husband did, and have noticed that people stared at me in an odd way.
I think you need to do simultaneous bench presses in order to get requisite tightening of the diaphragm.
We need more kings like Oscar II.
THANK YOU for this video! I always wondered why we can't make predictions even if we had perfect measuring devices as it's still a deterministic system. You answered every one of my questions!
In highly complex systems, emergent behaviors can form. I would say the difference is if its a learning system, where with time there some sort of fitness function that guides how the entire system progresses in time, and if its not a learning system. I would say its like the Logic in Sudoku. If you have a square in sudoku that either a 1 or a 2 narrowed down, if you assume 1 and see what other squares must be, or if its a 2 and you see where other squares must be, where they intersect you can know what that square is without knowing what the original square value is. You can do this in games like minesweeper as well. So you can jump logical if A or B is true, and if A then C is true, and if B then C is true, then you can know C is true without knowing A or B truth value. Makes a powerful tool to break the hardest Sudokus when experimenting with the logic. Then came up handy on occasion in minesweeper. So that a 3 body is bound to following some equation maybe half true. Under conditions it could converge to an emergent behavior even though it seems wildly chaotic, the chaos itself will have emergent behaviors, like for example entropy. Things these equations may not have in them. And where fundamental theory of all learning systems maybe able to in time give them the tools to make their functions much more capable. Like a PDE can give a function and path, but in reality some kind of evolution of the system will occur and gravitate towards repeatable patterns. So something maybe chaotic, but if Saddle point if it goes on A side, or the B side, there maybe future states C that occur from both. So you can know the truth value of C without knowing if it went left or right on the saddle point. But this logic form is incredibly difficult to work with even in Sudoku to break the hardest puzzles.
_Chaos is a ladder_
0:58 hehe... gravity
I'm glad someone noticed this
Sending this video to the Trisolarans so they leave us alone
Haha....clever play on the book.
Bravo for the clarity and the dynamic story. I am quantum physicist by training but worked the last 25 years in life sciences.
I love how your series is so well done that I can almost understand some of this stuff that I never could before.
i took several college physics classes, and i have NEVER heard of the 3-body problem until the Netflix TV show 😕
Same here. 4-5 years of engineering with the associated math/physics. Never knew this was a “problem.” Then the Netflix series showed up.
"Saddle Points" would make a good story term, for turning point decisions.
Well, we have the 8+ Body problem. With orbits in the Sol system attaining resonance (google metronome resonance), it is only a matter of time till one of the Planets gets pulled out of orbit, the Professionals believe that planet will be Mercury.
The sun is more than 1000 times more massive than the largest planet. Which is why the planets revolve around it
There's some ideas thrown around that the Solar system has already ejected a planet in such a way. Evidence (with wrinkles, as always) is mounting that suggests that a large number of stellar systems like Sol's do so.
Love the animations, a great explanation to intro nonlinear topics 😊💖💯
I actually got into this interesting mathematical discussion through synthesis, an instrument known as a chaos oscillator, based on the electronic circuit developed by Chuas. It’s a brilliant topic and I appreciate your ability to conceptualize ideas well beyond the orbit of my training and understanding. Thank you!
"It really was revolutionary"
I see what you did there.
I am early today it seems
I already watched 💀
sorry cannot concentrate. two body problem.
Excellent explanation. I don't think I've heard it explained so well. I have to admit the white dot shirt emblem had me a bit distracted. I was trying to figure out what that was!
your video on singularity was my first physics video on UA-cam. now I am hooked. apart from the occasional depression, I love them 😊
Incant stop looking at them
Amazing video. I have seen some videos about the three body problem, but this is the first one which explained why such motion is fundamentaly unpredictible. Thanks!
I feel like the answer to this is a) consider a heirarchy of mass. The heaviest object is always the primary mass, and as you get lighter and lighter, each one is a servant to the heavier mass. b) This of this in terms of spacial distortions. Once you know what the basic path each body should normally follow, around the heaviest mass, then you can build a distortion map. You can then figure out what happens to the distortions each time distortions from one map intersects with distortions from the other map.
I have watched a great many videos taking about the Three Body Problem and its unsolvability, but I never felt like I truly understood why until now. Great video, thank you!
I believe that something else should be considered, synchronicity.
There was an experiment conducted with boxes that have motors. Arms are attached to the motors. The arms are off center causing one end to swing out. Three such motors are placed so that the tips of the arms interfere with each other. The arms are random lengths and spin at random rates. When the tips happen to hit the motors reverse. After some time the three arms will find a way of bypassing each other regularly.
This could explain how the Sun, Earth and Moon have solved the three body problem astro-mechanically.
Enjoyable learning, well presented and paced as always. Must say though I never such an upbeat attitude and bright eyed enthusiasm in my physics class.
This is very different from another classic problem: You have 3 dead hitmen but only room in the trunk for two.
What to do, what to do?
Super video. Having seen some of the drawings.. I suspect if Kandinsky and Miro had teamed up to draw in black and white, they might well have struggled to match Poincaré's level of abstraction.
Very well explained with humorous animations and a pair of curious eyes! I like the part about deterministic predictability.
I love the way you graphically present this subject, making order on this hard to understand physics.
So go on making such videos!
I started in physics but switched to biology when my first modern physics class made me realize how dumb I actually am 😆. I still love physics but now I love it as a spectator now. You can't know how hard those problem sets are until you've actually worked on them, This channel is so great, thanks for making crazy hard stuff fun to learn about!
An excellent presentation! I would have been interested in a discussion of the stability of LaGrange points resulting from the gravity of 3 bodies.
The three body problem: when a couple have a child, the chaos sets in.
A really recommended beginners book to learn nonlinear dynamics and chaos from is Steven Strogatz’s “Nonlinear dynamics and chaos”. He also has a series of lectures on the topic here on UA-cam.
Sublimely beautiful explanation. Lovely description of the role of saddle points.
Beautiful presentation and explanation!
Wow... you really nailed communicating a complex topic in a way that is very easy to follow. Outstanding !
As someone who started out doing medicine, then switched to maths, and ultimately ended up doing mathematical epidemiology (which has a surprising amount in common with the topic you've been discussing here), I get how you felt about switching from biology to physics. Interestingly in my field a lot of people seem to have come from either maths or physics. Or veterinary science via statistics.
Great way to say "Henri Pointcarré" in French ! And you say it quite well! afterward). Great content. Thank you for sharing this video, as I hadn't historically connected Pointcarré's geometry to the 3 body problem.
beautifully done. I haven't seen chaos related to saddle points in such a clear way before. Obvious in retrospect, like most brilliant insights.
We are living in amazing times
We have digital tools that create visual images so clearly, that the equations can be seen as real images we can grasp in an instant.